The heater core can be replaced - however it's fairly involved and requires the steering wheel and instrument panel to be removed. The replacement parts are inexpensive - compared to a new vehicle. Try the heater core replacement and installation instructions - below.
Check out the many on-line auto parts sources; such as - www.partsgeek.com or www.rockauto.com - to list just two sources - for the replacement parts, such as the heater core and heater hoses. For example, they (Rock Auto) list the heater core for around $26.00 for your vehicle.
1) Disconnect the negative battery cable. Jack up the car and drain the engine coolant from the cooling system by placing a container underneath the radiator directly below the drain plug. Remove the plug with a crescent wrench, allow all the coolant to drain, replace the plug and properly dispose of the used fluid.
2) Remove the driver's side air bag. With the steering column in its lowest position, turn the wheel 90 degrees in each direction and twist a 7-inch screwdriver counterclockwise in the hub hole to release each air bag clip. Remove the bag with the wheel turned straight ahead.
3) Disconnect the steering wheel. With the tires facing straight ahead, disconnect the horn's electrical connector and remove the wheel-to-steering column bolt to remove the wheel.
4) Detach and remove the instrument panel. Start by removing the screws and connectors on the driver's side, including the steering column. Disconnect all side covers, the glove box, the radio and all electrical connectors. You'll need two people to remove the panel at the end.
5) Loosen the crossmember-to-chassis bolts from the instrument panel and lift up the crossmember. Disconnect the heater hoses from the core.
6) Take the heater core out of the heater/ventilation or air conditioning housing assembly. On a ventilation assembly, partially remove the assembly and the retainer clips. On an AC system, discharge the refrigerant, disconnect the refrigerant lines and remove the ventilation ducts.
7) Install the new heater core to the heater/air conditioning or ventilation housing assembly. Connect the assembly back into the VW Beetle, reconnecting the refrigerant lines (if they were disconnected and if it is safe to do so yourself) and heater hoses. Now is the time to replace the heater hoses and clamps with new ones.
8) Lower the crossmember and re-install the crossmember-to-chassis bolts for the instrument panel. Put the instrument panel back on (this may require an assistant).
9) Reinstall the steering wheel to the steering column and the air bag to the wheel.
10) Refill the cooling system and reconnect the negative battery cable. Evacuate, charge and leak test the air conditioner's refrigerant. (If your Beetle is equiped with R-12 refrigerant, then you can't complete this step yourself, and you'll need to take it to an EPA-certified technician.)
11) Start and operate the VW Beetle's engine to its normal operating temperature. Check the climate control operation and look for any leaks in the system.